Write the expression for equilibrium constant, K for each of the following:
(i)`C(s)+CO_2(g) hArr 2CO(g)`
(ii)`Na_2CO_3 (s)+SO_2(g) + 1/2O_2(g) hArr Na_2SO_4 (s)+CO_2(g)`
(iii)`PbI_2(s) hArr Pb^(2+)(aq)+2I^(-)(aq)`

Answer

To write the expressions for the equilibrium constant \( K \) for the given reactions, we need to follow the principles of chemical equilibrium. The equilibrium constant can be expressed in terms of concentrations (for aqueous solutions) or partial pressures (for gases). Here's how to derive the expressions for each reaction step by step:

### (i) Reaction:
\[ C(s) + CO_2(g) \rightleftharpoons 2CO(g) \]

**Step 1:** Identify the reactants and products.
- Reactants: \( C(s) \) and \( CO_2(g) \)
- Products: \( 2CO(g) \)

**Step 2:** Write the expression for \( K_p \).
- Since \( C \) is a solid, it does not appear in the equilibrium expression.
- The equilibrium constant \( K_p \) is given by the partial pressures of the gaseous products over the gaseous reactants.

**Step 3:** Write the expression:
\[ K_p = \frac{(P_{CO})^2}{P_{CO_2}} \]

### (ii) Reaction:
\[ Na_2CO_3(s) + SO_2(g) + \frac{1}{2}O_2(g) \rightleftharpoons Na_2SO_4(s) + CO_2(g) \]

**Step 1:** Identify the reactants and products.
- Reactants: \( Na_2CO_3(s) \), \( SO_2(g) \), and \( \frac{1}{2}O_2(g) \)
- Products: \( Na_2SO_4(s) \) and \( CO_2(g) \)

**Step 2:** Write the expression for \( K_p \).
- The solids \( Na_2CO_3 \) and \( Na_2SO_4 \) do not appear in the equilibrium expression.
- The equilibrium constant \( K_p \) is given by the partial pressures of the gaseous products over the gaseous reactants.

**Step 3:** Write the expression:
\[ K_p = \frac{P_{CO_2}}{P_{SO_2} \cdot (P_{O_2})^{1/2}} \]

### (iii) Reaction:
\[ PbI_2(s) \rightleftharpoons Pb^{2+}(aq) + 2I^{-}(aq) \]

**Step 1:** Identify the reactants and products.
- Reactants: \( PbI_2(s) \)
- Products: \( Pb^{2+}(aq) \) and \( 2I^{-}(aq) \)

**Step 2:** Write the expression for \( K_c \).
- The solid \( PbI_2 \) does not appear in the equilibrium expression.
- The equilibrium constant \( K_c \) is given by the concentrations of the aqueous products.

**Step 3:** Write the expression:
\[ K_c = [Pb^{2+}] \cdot [I^{-}]^2 \]

### Summary of Equilibrium Constant Expressions:
1. \( K_p = \frac{(P_{CO})^2}{P_{CO_2}} \)
2. \( K_p = \frac{P_{CO_2}}{P_{SO_2} \cdot (P_{O_2})^{1/2}} \)
3. \( K_c = [Pb^{2+}] \cdot [I^{-}]^2 \)